Physics 1 Unit 4 Practice Problems

Physics 1 Unit 4 Practice Problems The problems in this packet are here to help you practice some typical College‐Board style multiple‐choice questions you may see on the actual test, as well as some calculation‐based questions you may encounter along the way. Answers are available at the end of this document, so you need to show your work and explain the ideas behind your answer choices for full credit. Additionally, there is a space for you to write down your original answers (before checking your work) so that you can keep track of which types of problems might be challenging for you. Make sure you understand the following equations and know when to use them: W = Fd cos θ KE = ½ mv2 Wnet = ΔE P = W / t = F*v PEgrav = mgh Part 1 (4.A-4.H: Work and Conservation of Energy) Question My Answer Right Answer 1 2 3 4 5 6 7 8 PEspring = ½ kx2 PEgrav = -GMm / r Part 2 (4I-4O: Energy Conservation and Power) Question My Answer Right Answer 9 10 11 12 13 14 15 Part 1 (Topics 4.A-4.H: Work and Conservation of Energy) 1. A force F is exerted on a 5 kg block to move it across a rough surface, as shown above. The magnitude of the force is initially 5 N, and the block moves at a constant velocity. While the block is moving, the force is instantaneously increased to 12 N. How much kinetic energy does the block now gain as it moves a distance of 2 m across the rough surface? (a) 10 J 2. (b) 14 J (c) 24 J (d) 34 J Find the net work done on a box if it is pulled 5 meters across the floor using a cord with a tension of 60 N at an angle of 30 degrees from horizontal while friction applies a constant force of 5 N. (a) 55 J (b) 235 J (c) 260 J (d) 275 J (e) 285 J 3. A 1000-kg car (including the driver) traveling 20 m/s goes around a 125 m radius semicircular curve at constant speed, traveling a distance of 125π meters. What is the work done by friction on the car as the car makes the turn? (a) 0 J (b) 125,000π J (c) 400,000 J (d) 800,000 J (e) 400,000π J 4. A student is asked to move a box from ground level to the top of a loading dock platform, as shown in the figure. In Figure 1, the student pushes the box up an incline with negligible friction . In Figure 2, the student lifts the box straight up from the ground level to the loading dock platform. In which case does the student do more work on the box? In which case does the student use more force to get the box to the desired position? 5. An object with mass m is suspended at rest from a spring with a spring constant of 200 N/m. The length of the spring is 5.0 cm longer than its unstretched length L, as shown. A person then exerts a force on the object and stretches the spring an additional 5.0 cm. What is the total energy stored in the spring at the new stretched length? (a) 0.25 J 6. (c) 10 J (d) 20 J (e) 100 J (Extra Practice #2) A force F at an angle θ above the horizontal is used to pull a heavy suitcase of weight mg a distance d along a level floor at constant velocity. The coefficient of friction between the floor and the suitcase is µ. The work done by the frictional force is: (a) -Fd cos θ 7. (b) 1 J (b) - µ Fd cos θ (c) - µmgd (d) - µmgd cos θ Two blocks of the same mass, but made of different material, slide across a horizontal, rough surface and eventually come to rest. A graph of the kinetic energy of each block as a function of position along the surface is shown. Which of the following is a true statement about the frictional force Ff that is exerted on the two blocks? (a) Ff2 = 2 Ff1 because the force of friction is represented as the slope for each of the two curves. (b) Ff2 = 1/2 Ff1 because the force of friction is represented as the inverse slope for each of the two curves. (c) Ff2 = 2 Ff1 because the force of friction is represented as the inverse of the area bound by each curve and the horizontal axis. (d) Ff2 = 1/2 Ff1 because the force of friction is represented as the area bound by each curve and the horizontal axis. 8. (Complete this AFTER working through Student Workbook 4.H.) A 1 kg block is attached to a spring with spring constant k = 40 N/m. The rest length of the spring is 0.25 m. The mass is dropped so that it stretches the spring until it slows to a stop. Calculate the total length of the spring when the mass is in equilibrium (no net force) and the length of the spring when the mass comes to a stop. Part 2 (Topics 4.I-4.O: Energy Applications and Power) 9. You learned in the last unit that there is a minimum speed at which a rollercoaster can go around a loop and still maintain contact with the track. What is the minimum height h the car should be released so that it goes around the loop safely? Express your answer in terms of only R. (Hint: Use both Conservation of Energy and Centripetal Force equations to write two expressions like “mv2 = …") (a) h = 3R/2 (b) h = 2R (c) h = 5R/2 (d) h = 3R (e) h = 5R 10. Two masses m1 and m2 are connected by a massless string and pulley (m1 < m2). The objects are released from rest, and mass m2 descends a distance h. Find the final speed of the mass m2. (Stuck? See Extra Practice #29.) 11. The roller coaster car below is pulled up to point 1 and released from rest. Assuming no friction, calculate the speed of the car at points 2, 3, and 4. (Numerical answers – no multiple choice for this question.) 12. A block of mass m is attached to a spring of spring constant k. The mass is given an initial displacement x0 from the equilibrium, and an initial speed of v 0. Using energy methods, determine A) the total mechanical energy of the block-spring system, B) the maximum speed of the block, and C) the maximum displacement of the block. (No multiple choice for this question.) 13. (Extra Practice #24) What is the kinetic energy of a satellite of mass m that orbits the Earth, of mass M, in a circular orbit of radius R? 14. A block of mass m is pushed up a ramp at an angle θ above the horizontal by a horizontal force F without friction. Find the kinetic energy of the mass after it has traveled a distance d up the ramp. 15. A toy car engine has a power output of 3 W, meaning every 1 second of operation it can convert 3 J of chemical energy into mechanical energy. Friction applies a constant force of 0.5 N opposing the motion of the car. What is the highest speed the car can travel while still providing enough energy to match the energy loss due to friction? (a) 1.5 m/s (b) 3 m/s (c) 4.5 m/s Answer Key: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. B B A C B A A C C A Point 2: 25.0 m/s, Point 3: 10.8 m/s, Point C: 18.8 m/s 12. 13. A 14. A 15. D (d) 6 m/s (e) 18 m/s